Nuprl Lemma : names-deq_wf
∀[I:fset(ℕ)]. (NamesDeq ∈ EqDecider(names(I)))
Proof
Definitions occuring in Statement :
names-deq: NamesDeq,
names: names(I),
fset: fset(T),
deq: EqDecider(T),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
names-deq: NamesDeq,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
names: names(I),
so_lambda: λ2x.t[x],
nat: ℕ,
so_apply: x[s]
Lemmas referenced :
int-deq_wf,
strong-subtype-deq-subtype,
names_wf,
strong-subtype-set3,
nat_wf,
fset-member_wf,
le_wf,
strong-subtype-self,
fset_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
hypothesis,
applyEquality,
thin,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
intEquality,
independent_isectElimination,
lambdaEquality,
because_Cache,
natural_numberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[I:fset(\mBbbN{})]. (NamesDeq \mmember{} EqDecider(names(I)))
Date html generated:
2016_05_18-AM-11_56_18
Last ObjectModification:
2015_12_28-PM-03_08_52
Theory : cubical!type!theory
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